It should be noted that most of the measurements are using EM radiation, although the cosmological parameters can be measured precisely from various astronomical observations. Schuts first proposed that [1]}, using the fact that the waveform signals of GWs from inspiraling and merging compact binaries encode distance information, the Hubble constant can be determined from GW observations. So, this type of GW sources can be considered as standard sirens in astronomy, analogous to SNIa standard candles. Compared with the distance estimation from SNIa measurements, the LDs can be obtained directly from the GW signals without the need of a cosmic distance ladder since stand sirens are self-calibrating. It is more important that GWs are able to propagate freely through a perfect fluid without any absorption and dissipation in the Friedman-Lemaître-Robertson-Walker metric. Therefore, most objects (e.g. the Earth) are
nearly transparent to GWs [2]} and the standard siren can be considered as an opacity-free distance indicator. Generally speaking, it is hard to obtain the redshift of the GW source. But the source redshift might be obtained from the observation of EM counterparts that occur coincidentally with the GW events [3]}, [4]}, [5]}, [6]}, if compact binaries are neutron star (NS)-NS or black hole (BH)-NS binaries. Recently, the joint detection of GW event GW170817 with EM counterpart (GRB 170817A) from the merger of binary NSs [7]}, [8]}, [9]}, [10]} opened a new era of multi-messenger cosmology. Thus, the LD-redshift relation can be constructed by a cosmological model-independent way, and it can be used to make constraints on the parameters of cosmology.
